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Hilbert’s Inferno

Hell may be the most interesting part of Dante’s famous poem, but its physical existence has always been a topic of debate among philosophers and theologians. If either space or time is finite—a distinct possibility in our current theories of cosmology—how can there be room for a potentially infinite number of sinners for eternity? In what he admits is a speculative proposal, University of Edinburgh philosopher Alasdair Richmond suggests that a hell large enough for an infinite number of the damned could be contained within the boundaries of a finite space, and could provide infinitely-long punishment, even if time itself is finite—but only with the help of time travel. The quite literally devilish trick is a kind of time loop, but not an exact loop. (That would mean that the damned merely suffer through the same experience over and over, without any awareness of the eternal nature of their plight—which is not suffering enough for the traditional idea of Hell.) If the loop shifts and the gap shrinks just the tiniest bit each time around, you end up with an ever-tightening time spiral. You can fit an infinite number of spirals in a tiny amount of space the same way an infinite number of points lie between any two other points on a line. This hell, which Richmond calls “Hilbert’s Inferno” (for pioneering mathematician David Hilbert), might deliver truly eternal torment to an infinite population of sufferers, while the non-suffering and temporally finite universe moves steadily onward, toward its own non-judgmental doom.

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